There are many ways to test your computers memory but, if your running Windows Vista you have a built-in option.

Using the Memory Diagnostic Tool you can check your physical RAM, which can often be the cause of random crashing in Windows.

OK lets get started. First click on the "Start" button and type in "memory" in the search box like the picture below.

Then click on Memory Diagnostic Tool and continue through the uac nag screens and you will end up with this option.

I suggest to go ahead and click Restart now and check for problems. Windows will restart the computer automatically and begin testing the computer memory. The Memory Diagnostic Tool has three modes : Basic, Standard and Extended tests which can be accessed by pressing "F1" during the test and then "F10" to apply(by default Windows will perform a STANDARD test). After all the tests have been completed Windows will display the results of the test after you log on.